How to create a Life Preserver style texture?
Since you don't want to correctly unwrap each new object we need a procedural shader which uses the angle from the objects origin.





That way you can easily displace and distort without worrying about the UV.

First we need an atan2 node to calculate the circular angle as viewed from top.



It is show in the red atan2 box in the node overview. You can also find explanations here. I used the nodes in the first answer. Group them into the atan2 group.

(We'd manage with a simple arctangent node from cycles, but it doesn't hurt to have an atan2 in your library and it's not that complex.) 

Use the objects X and Y coordinates as input.



Right now the values and in the range [-pi, pi]. Let's normalize them by adding pi and diving by 2*pi.



After that, multiply by the number of intersections you wish, and add the modulo and greather than to get separations of 0 and 1.



At this point, it would be smart to group the nodes into a rings group. That way, when we make this material a single user to change the colors or the amount of sections all materials will use the same ring group.